Title: Auf Wiedersehen Surfaces, Revisited
Speaker: Robert Bryant
Speaker Info: MSRI and University of California, Berkeley
Brief Description:
Special Note:

It has been known for over a century that there are many Riemannian metrics on the 2-sphere with the property that all of their geodesics are closed. Zoll, a student of Hilbert, constructed an infinite dimensional family of surfaces of rotation with this property. Following ideas of Funk, Guillemin proved that these metrics on the 2-sphere are essentially parametrized by the odd functions on the round 2-sphere.

These ideas can also be applied to the understanding of Finsler metrics on the 2-sphere whose Finsler-Gauss curvature is constant, as will be explained in the talk. This leads, via the recent work of LeBrun and Mason, to a resolution of a basic problem in Finsler geometry: to describe such Finsler metrics on the 2-sphere.

In this talk, no knowledge of Finsler geometry will be assumed, only a very basic understanding of curves and surfaces. The history of the problem will be discussed, and numerous examples will be given to illustrate the underlying ideas.

Date: Wednesday, March 10, 2010
Time: 4:10pm
Where: Lunt 105
Contact Person: Ezra Getzler
Contact email: getzler@northwestern.edu
Contact Phone:
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